"I did an internship" seems the most natural way to say this.

I did is the best international English choice.

I took does not tell us if you were successful or failed or left.

I attended does not tell us how many lectures, talks, seminars, classes, lessons, meetings or whatever that you attended.

I had an internship begs the question what happened to the internship? and why haven' you got one now?.

I did = usually completed, but you might not have done.

This is one of those occasions when a longer sentences is required, to clarify the situation.

For job applications etc go with.

I completed my internship at the X for the Y certificate whatever etc.

I completed my internship at the X to receive/be awarded the Y certificate whatever etc.

Thank you all!

John, perfect explanation!!

I believe that "I did an internship" would be the most natural way of putting it in American English as well.

Hey girl! At Least here in the US, either verb would make perfect sense. I personally would say "I had an internship with ...". But all of those verbs would work well :)